Problem: What's the first wrong statement in the proof below that $ \triangle EBC \cong \triangle EBD$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. A B C D E F Givens $ \angle ACB \cong \angle BDE$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ $ \overline{AB} \cong \overline{BE}$ $, \ $ $ \overline{EF} \cong \overline{BE}$ $, \ $ $ \angle CFE \cong \angle DBE$ $, \ $ and $\ $ $ \overline{CF} \cong \overline{BD}$ Proof $ \triangle EBD \cong \triangle EFC$ because SAS $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle EBD \cong \triangle ABC$ because AAS $ \overline{BD} \cong \overline{BC}$ because corresponding parts of congruent triangles are congruent $ \triangle EBD \cong \triangle EBC$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. There is no wrong statement in this proof.